90 On the Laws of Crystalline 



ether to be the same in all media.* At the same time I was 

 compelled to employ the principle of equivalent vibrations, in 

 order to have a sufficient number of conditions, though for a 

 while I overlooked the perfect agreement which now subsisted 

 between this principle and the law of vis viva : it happened, in 

 fact, that the new hypothesis of a constant density made the 

 vis viva of the refracted ray exactly the same as in the theory 

 of Fresnel.f 



But to see why it was necessary to assume the principle of 

 equivalent vibrations, we must observe, that when a polarized 

 ray is incident on a crystal there are four things to be deter- 

 mined, namely, the direction and magnitude of the reflected 

 vibration, and the magnitudes of the two refracted vibrations. 

 Hence we must have four conditions, or we must have relations 

 affording so many equations. But the hypotheses of Fresnel, 

 by which he solved the problem of reflexion for ordinary media, 

 afford only three conditions. We will state his hypotheses at 

 length : 



1st. The vibrations of polarized light are in the plane of the 

 wave, and perpendicular to the plane of polarization. 



2nd. The density of the ether is inversely as the square of 

 the refractive index of the medium. 



3rd. The vis viva is preserved. 



4th. The vibrations parallel to the separating surface of two 

 media are equivalent; that is, the refracted vibration parallel to 

 the surface is the resultant of the incident and reflected vibra- 

 tions parallel to the same. 



We see that the fourth hypothesis gives two conditions, and 

 the law of vis viva gives a third. 



Let us now take the more general principle of equivalent 

 vibrations, in place of the fourth hypothesis of Fresnel, altering 



* This hypothesis is maintained by Mr. Challis ; and certainly it falls in ex- 

 tremely well with the astronomical phenomenon of the aberration of light. See, 

 on this subject, Professor Lloyd's Report on Physical Optics, " Fourth Report of the 

 British Association for the Advancement of Science," pp. 311, 313. 



t Supra, p. 100, note. 



